You've got an array consisting of n integers: a[1], a[2], ..., a[n]. Moreover, there are m queries, each query can be described by three integers l i , r i , k i . Query l i , r i , k i means that we should add to each element a[j], where l i ≤ j ≤ r i . Record means the binomial coefficient, or the number of combinations from y elements into groups of x elements. You need to fulfil consecutively all queries and then print the final array.

输入描述:

The first line contains integers n, m (1 ≤ n, m ≤ 105).The second line contains n integers a[1], a[2], ..., a[n] (0 ≤ ai ≤ 109) — the initial array.Next m lines contain queries in the format li, ri, ki — to all elements of the segment li... ri add number (1 ≤ li ≤ ri ≤ n; 0 ≤ k ≤ 100).

输出描述:

Print n integers: the i-th number is the value of element a[i] after all the queries. As the values can be rather large, print them modulo 1000000007(109 + 7).